Metric Space Magnitude for Evaluating the Diversity of Latent Representations
Abstract
The magnitude of a metric space is a novel invariant that provides a measure of the 'effective size' of a space across multiple scales, while also capturing numerous geometrical properties, such as curvature, density, or entropy. We develop a family of magnitude-based measures of the intrinsic diversity of latent representations, formalising a novel notion of dissimilarity between magnitude functions of finite metric spaces. Our measures are provably stable under perturbations of the data, can be efficiently calculated, and enable a rigorous multi-scale characterisation and comparison of latent representations. We show their utility and superior performance across different domains and tasks, including (i) the automated estimation of diversity, (ii) the detection of mode collapse, and (iii) the evaluation of generative models for text, image, and graph data.
Keywords
Cite
@article{arxiv.2311.16054,
title = {Metric Space Magnitude for Evaluating the Diversity of Latent Representations},
author = {Katharina Limbeck and Rayna Andreeva and Rik Sarkar and Bastian Rieck},
journal= {arXiv preprint arXiv:2311.16054},
year = {2025}
}
Comments
Accepted at the 38th Conference on Neural Information Processing Systems (NeurIPS) 2024. The code for computing magnitude is available at https://github.com/aidos-lab/magnipy